Radars are object-detection systems that use radio waves transmitted and received by an antenna to determine the range, angle, and/or velocity of objects. In most modern systems, radars employ an array antenna consisting of multiple antenna elements that are arranged and interconnected to form an individual antenna. In operation, the phase difference between the signals received by the antenna elements is measured and used to establish the signal arrival direction. For example, if the antenna elements are located on a planar surface and if the signal arrives normal to the surface, then the signal outputs of each antenna element are in phase, and the relative phase difference between the elements is ideally zero. If the signal arrives obliquely to the plane, the phase differences between the elements vary depending on the signal frequency, the distance between the antenna elements, and signal direction. In other words, due to the difference in propagation distances from the signal source to the individual antenna elements, each antenna element observes a different phase shift of the signal. This phase shift can then be used to determine the arrival direction of the incoming signal.
There are a number of known methods for determining the angle of arrival of an incident signal based on the phase difference between antenna elements. The basic relationship, however, is best explained by examining a two element linear array 10, as shown in FIG. 1. The antenna elements 12a, 12b are spaced apart by a distance “d” and the angle of arrival of the incident signals 14 forming wave front 16 is θ, which has a span of 180°. The arrival angle θ is referenced from an axis perpendicular to the plane of the array (i.e., broadside to the array) and ranges in angle from π/2 to −π/2 (90° to −90°). In an array designed to radiate broadside to the antenna array, the radiation pattern is at a minimum at π/2 and at −π/2 (90° and −90°), and becomes a maximum broadside to the array at 0 (0°). As understood by those skilled in the art, the angle of arrival can also be referenced from the axis of the array. In that case, θ still has a span of 180°, but instead ranges from 0 to π (0° to 180°) with minimums at 0 and π (0° and 180°) and a maximum at π/2 (90°).
Antenna arrays are directional in that they are designed to focus the antennas radiation pattern towards a particular direction by combining the antenna elements with phase adjustments that are a function of the direction of arrival. The direction of the radiation pattern is given by the main beam lobe, which is pointed in the direction where the bulk of the radiated power travels. The directivity and gain of an antenna array can be expressed in terms of the antenna's normalized field strength and array factor, which are fundamental principles of antenna array theory and well known in the art. For example, referring again to FIG. 1, the normalized field strength E(θ) at an angle θ measured off broadside is proportional to (sin NΨ/2)/(N sin Ψ/2), where N is the number of antenna elements in the array, Ψ is the phase difference between adjacent antenna elements and is equal to 2πd/λ(sin θ), wherein λ is the wavelength and d(sin θ) represents the linear distance of the propagation delay of the wave front 16 between adjacent antenna elements. The angle of arrival θ of the incident signals 14 can therefore be determined by knowing the phase difference Ψ.
A problem arises, however, because the phase between the elements can only be measured without ambiguity over a 180° range. When the antenna elements are widely-spaced (i.e., when distance between antenna elements exceeds one half of the wavelength of the incident signal), the phase difference between antenna elements can span more than 360°. Consequently, more than one possible arrival of arrival can be obtained and are commonly referred to as ambiguities.
The ambiguities caused by widely-spaced antenna arrays result in grating lobes, which refer to a spatial aliasing effect that occurs when radiation pattern side lobes become substantially larger in amplitude, and approach the level of the main lobe. Grating lobes radiate in unintended directions and are identical, or nearly identical, in magnitude to the main beam lobes. For example, referring above to the normalized field strength equation E(θ), a maxima occurs when the denominator is zero, or when sin θ=±n/(d/λ) where n =0, 1, 2, 3 . . . In arrays where the spacing between antenna elements d is equal to half the wavelength, the array produces a single maximum (i.e., main lobe) in the visible region of the array in the direction θ=0°. In arrays where the spacing between antenna elements d is greater than half the wavelength, additional maxima appear in the visible region at angles other than the direction of the main lobe. For instance, when the spacing between antenna elements is 2λ, the main lobe appears at θ=0°, but grating lobes also appear at θ=±30° and ±90°. Because each of these angles corresponds to a maxima, the radar system in not capable of distinguishing between the angle of arrival corresponding to the main lobe and the angles of arrival corresponding to the grating lobes. Stated another way, a single phase measurement may refer to multiple angles of arrival resulting in additional ambiguities.
Antenna arrays are generally designed for optimum directivity with high angular resolution. However, angular resolution is proportional to the size of the antenna aperture and the number of antenna elements. High angular resolution requires a large aperture with a large number of antenna elements, which increases the cost of the antenna. In addition, the size of the aperture and number of elements is limited by the antenna element spacing due to phase ambiguities. The method described hereinafter resolves the problem of phase ambiguities associated widely-spaced antenna arrays, thereby achieving unambiguous high angular resolution with a reduced number of channels. A significant cost reduction is realized by the reduction of antenna elements used in the array.